The application of probabilistic methods on estimating the asympotic behavior of multigraph Ramsey function

The multigraph Ramsey number is a natural generalization of the classical Ramsey number, given by generalizing the edge coloring of simple complete graphs to the edge coloring of complete multigraphs. Computing values of Ramsey numbers is NP hard, and it is even difficult to compute the values of multigraph ones, but probabilistic methods are always efficient ways to research Ramsey theory. In this paper, the application of probabilistic methods on estimating multigraph Ramsey number are briefly introduced, the asymptotic lower bounds and parameter lower bounds for multigraph Ramsey number are proposed by the probabilistic, and the upper bounds for multigraph Ramsey number is put forward by induction finally.